independent and absorbent subsets of bi-algebras

In this paper, we define the notion of the right independent (resp., left independent) subsets of bi-algebras. some of the properties are investigated and get more results in bi-algebras. moreover, we consider the notion of the right absorbent (resp., left absorbent) subset. it is proved that in a right distributive bi-algebra x, every right(left) independent subset of x absorbs x from the right. we show that these new concepts are different by presenting several examples. the goal and benefits of our proposed extension of this study are to extend the theory of bi-algebras, and so we enlarge the field of research.